Heat oil in a large sauté pan over medium high and add ground beef. Cook for 8 to 10 minutes or until nicely browned. Add onions and cook 4 minutes more. Add mushrooms and cabbage and cook for 5 minutes or until wilted. Remove from heat and stir in soy sauce, pepper, chili garlic sauce and sesame oil. Set aside until cool enough to work with.
Lay one egg roll wrap in front of you with a tip pointing down. Spoon about 3 tablespoon of filling into the middle of the wrap. Lightly brush each corner with egg wash. Fold bottom corner up and over the filling, tuck each side in and continue to roll up, sealing tightly. Place on a baking sheet, seam side down.
Fill a large skillet a 1/4 inch deep with oil and heat over medium to medium-low heat. Fry egg rolls about 5 minutes until crispy and golden brown on all sides, using tongs to turn them so they brown evenly.